Name
Abstract | ||
|---|---|---|
The Matern family of functions is a widely used covariance kernel in spatial statistics for Gaussian process modeling, which in many instances requires calculations with a covariance matrix. In this paper, we design a fast summation algorithm for the Matern kernel in order to efficiently perform matrix-vector multiplications. This algorithm is based on the Barnes-Hut tree code framework and addresses several practical issues: the anisotropy of the kernel, the nonuniform distribution of the point set, and a tight error estimate of the approximation. Even though the algorithmic details differ from the standard tree code in several aspects, empirically the computational cost of our algorithm scales as O(n log n) for n points. Comprehensive numerical experiments are shown to demonstrate the practicality of the design. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1137/120903002 | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
Keywords | Field | DocType |
Matern kernel,Gaussian process,fast summation,tree code | Kernel (linear algebra),Spatial analysis,Mathematical optimization,Kernel principal component analysis,Gaussian process,Covariance matrix,Time complexity,Variable kernel density estimation,Mathematics,Covariance | Journal |
Volume | Issue | ISSN |
36 | 1 | 1064-8275 |
Citations | PageRank | References |
2 | 0.39 | 10 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jie Chen | 1 | 2487 | 353.65 |
| Lei Wang | 2 | 21 | 2.17 |
| Mihai Anitescu | 3 | 421 | 43.56 |